Joanne sets up her teenage mutant ninja turtles in a big circle, spacing each turtle at an equal distance from its neighbors. She then begins counting them in order around the circle, but she loses track of where she started before she finishes counting. Then she notices that the sixth turtle is directly opposite the seventeenth turtle, and she realizes that she can still figure out how many turtles are in the circle. How many turtles are in the circle?